Mathematics
Grade 5
15 min
Properties of addition
Properties of addition
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1
Introduction & Learning Objectives
Learning Objectives
Identify and define the Commutative Property of Addition.
Apply the Commutative Property to reorder addends for easier calculation.
Identify and define the Associative Property of Addition.
Apply the Associative Property to group addends for more efficient addition.
Identify and define the Identity Property of Addition.
Use the Identity Property to simplify expressions involving zero.
Explain how using properties of addition can simplify mental math.
Have you ever wondered if changing the order of numbers when you add them makes a difference? 🤔 Let's find out how special rules can make addition easier!
In this lesson, you'll discover three powerful properties of addition: Commutative, Associative, and Identity. Understanding these properties...
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Key Concepts & Vocabulary
TermDefinitionExample
Commutative Property of AdditionThis property states that changing the order of the numbers (addends) in an addition problem does not change the sum.If you add 3 + 5, you get 8. If you add 5 + 3, you also get 8. So, 3 + 5 = 5 + 3.
Associative Property of AdditionThis property states that when you add three or more numbers, the way you group the numbers (using parentheses) does not change the sum.If you add (2 + 3) + 4, you get 5 + 4 = 9. If you add 2 + (3 + 4), you get 2 + 7 = 9. So, (2 + 3) + 4 = 2 + (3 + 4).
Identity Property of AdditionThis property states that the sum of any number and zero is that number itself. Zero is called the additive identity.If you add 7 + 0, you get 7. If you add 0 + 15, you get 15. So, 7 + 0 = 7.
AddendA number that is added to another...
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Core Formulas
Commutative Property of Addition
$a + b = b + a$
You can swap the order of any two numbers being added, and the total will remain the same. This is useful for reordering numbers to make mental math easier.
Associative Property of Addition
$(a + b) + c = a + (b + c)$
When adding three or more numbers, you can group them in different ways using parentheses without changing the sum. This helps in combining numbers that are easy to add first.
Identity Property of Addition
$a + 0 = a$
Adding zero to any number does not change the value of that number. Zero is the 'identity' element for addition.
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Challenging
Leo says the equation (10 + 5) + 2 = 10 + (2 + 5) demonstrates the Associative Property. Why is his reasoning incomplete?
A.He is correct; only the Associative Property was used.
B.He is incorrect; only the Commutative Property was used.
C.His reasoning is incomplete because both the Commutative and Associative properties were used.
D.He is incorrect because the equation is false.
Challenging
Which statement best explains the fundamental difference between the Commutative and Associative Properties of Addition?
A.Commutative involves two numbers and Associative involves three or more numbers.
B.Commutative is about the order of addends, while Associative is about the grouping of addends.
C.Commutative works with parentheses, while Associative does not.
D.Commutative is used for mental math, while Associative is used for written math.
Challenging
Which equation is the BEST example of using the Commutative Property to simplify mental math?
A.1/2 + 1/4 = 1/4 + 1/2
B.10 + 20 = 20 + 10
C.99 + 1 = 1 + 99
D.13 + 88 + 87 = 13 + 87 + 88
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